Optical scanning lens, optical scanning device and image forming apparatus

ABSTRACT

An optical scanning lens which is used in a scanning and age forming optical system which gathers a light flux deflected by a light deflector in the vicinity of a surface to be scanned. The lens is formed by plastic molding of polyolefin resin, and the following condition is satisfied: 0&lt;|Δn(x)−min [Δn(x)]|&lt;34×10 −5 , where Δn(x) denotes a refractive-index distribution existing inside the lens, in a range which the light flux passes through, in the lens, and min [Δn(x)] denotes the minimum value of the Δn(x).

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention generally relates to an optical scanninglens, an optical scanning device and an image forming apparatus.

[0003] 2. Description of the Related Art

[0004] An optical scanning device, which deflects a light flux from alight source at a uniform angular velocity by a light deflector having adeflection reflecting surface, converges the deflected light flux on asurface to be scanned as a beam spot by a scanning and image formingoptical system, and, thus, scans the surface to be scanned at a uniformvelocity with the beam spot, is well-known in relation to ‘image formingapparatus’ such as a digital copier, an optical printer, a laserplotter, a digital plate maker and so forth.

[0005]FIG. 1 illustrates one example of an optical scanning device.

[0006] A divergent light flux emitted by a semiconductor laser 10 istransformed into a light flux form (such as a parallel light flux or thelike) suitable for subsequent optical systems by a coupling lens 12,passes through an opening of an aperture 14 so as to undergo ‘beamformation’, and is reflected by a mirror 18, while being converged insub-scanning directions by a cylinder lens 16, and an approximatelyline-like image long in main-scanning directions is formed in thevicinity of a deflection reflecting surface of a rotational polygonalmirror 20. The light flux reflected by the deflection reflecting surfaceis incident on a scanning and image forming optical system 30 whilebeing deflected at a uniform angular velocity as the rotationalpolygonal mirror 20 rotates at a uniform velocity, and is gathered inthe vicinity of a surface to be scanned (actually, a photosensitivesurface of a photoconductive photosensitive body or the like) 40 by afunction of the optical system 30, and, thereby, a beam spot is formedon the surface to be scanned 40. By the beam spot, the surface to bescanned 40 is scanned in main scanning directions. The photosensitivesurface which embodies the surface to be scanned 40 is moved in asub-scanning direction (direction perpendicular to the plane of FIG. 1),and, the above-mentioned optical scanning is repeated. Thereby, a latentimage is written on the photosensitive surface. A velocity of theabove-mentioned optical scanning by a beam spot is made uniform by afunction of a velocity uniformizing character of the scanning and imageforming optical system 30.

[0007] Throughout the specification and claims, ‘an optical scanninglens’ is used in the above-described scanning and image forming opticalsystem. In the example FIG. 1, the scanning and image forming opticalsystem 30 consists of a single lens. In this case, the scanning andimage forming optical system 30 itself is an optical scanning lens. Whena scanning and image forming optical system consists of a plurality ofoptical elements (a plurality of single lenses, a lens and a concavemirror or the like), one or a plurality of single lenses used therein isan optical scanning lens.

[0008] As an optical scanning lens used in a scanning and image formingoptical system, a lens obtained as a result of molding of plasticmaterial has been used.

[0009] One problem occurring when an optical scanning lens is formed bymolding plastic material is that a refractive-index distributiondevelops inside the thus-formed optical scanning lens.

[0010] In plastic molding, a plastic material, melted by heat, is moldedby a metal die, and is cooled in the metal die. In this process, coolingof the material is fast in the periphery in comparison to the middle ofthe metal die. Thereby, a non-uniform distribution (the density of afast-cooled portion is higher than the density of a slowly-cooledportion) in density and/or modification develops in the plastic.Thereby, the refractive index of the thus-formed lens is not uniform,and, thus, a refractive-index distribution develops therein.

[0011]FIGS. 2A through 2E illustrate such a refractive-indexdistribution. FIG. 2A shows a refractive-index distribution of anoptical scanning lens 30 as a scanning and image forming optical systemshown in FIG. 1 by contour lines in a section taken along a planeincluding the optical axis thereof and parallel to main scanningdirections, and FIG. 2B shows a refractive-index distribution of thatshown in FIG. 2A in directions perpendicular to the optical axis andparallel to the main scanning directions. FIG. 2C shows arefractive-index distribution of the optical scanning lens 30 by contourlines in a section taken along a plane including the optical axisthereof and parallel to sub-scanning directions, FIG. 2D shows arefractive-index distribution of that shown in FIG. 2C in directionsparallel to the optical axis (axial directions), and FIG. 2E shows arefractive-index distribution of that shown in FIG. 2C in directionsperpendicular to the optical axis and parallel to the sub-scanningdirections.

[0012] As shown in FIGS. 2B, 2D and 2E, a refractive-index distributionin a plastic-molded lens is such that, generally, a refractive index ata peripheral portion of the lens is higher than that at a middle portionthereof.

[0013] Generally, when an optical scanning lens has such arefractive-index distribution inside thereof, actual opticalcharacteristics thereof differ somewhat from ‘design opticalcharacteristics of the optical scanning lens designed assuming that arefractive index therein is uniform’.

[0014] For example, when an optical scanning lens has a positive power,on average, a refractive index of a peripheral portion of the lens ishigher than a refractive index of a middle portion thereof, and, such arefractive-index distribution functions to shift an actual position atwhich a beam spot to be formed on a surface to be scanned is formed‘indirection in which the position goes away from a light deflector froma position determined in accordance with a design’.

[0015] A diameter of a beam spot by which an effective scanning range ofa surface to be scanned is scanned changes as an image height changesdepending on a curvature of field of an optical scanning lens. However,when a lens has such a refractive-index distribution therein, a diameterof a beam spot changes also due to an influence of the refractive-indexdistribution.

[0016] In FIG. 4, a vertical axis indicates a diameter of a beam spotand a horizontal axis indicates an amount of defocus (a differencebetween a position at which an image of a beam spot is formed (at whicha light flux is gathered) and a position of a surface to be scanned).The vertical axis coincides with a surface of a photosensitive body asthe surface to be scanned.

[0017] When an optical scanning lens has no refractive-indexdistribution therein and ‘a refractive index of the lens is uniformthroughout the lens’, a relationship between an amount of defocus and adiameter of a beam spot is such that, as indicated by a broken line, thediameter of the beam spot is minimum at a position of a surface to bescanned (a position at which the amount of defocus is zero, actually, aposition of a photosensitive body). However, when a refractive-indexdistribution exists, a relationship between an amount of defocus and adiameter of a beam spot is such that, as indicated by a solid line, thediameter of the beam spot at a position of a surface to be scanned islarger than that in accordance with a design (a cross point of thevertical axis and the broken line) due to ‘beam thickening’.

[0018] As materials of optical plastic lenses, mainly, acrylic resin, PC(polycarbonate) and polyolefin resin are known. Acrylic resin includesPMMA and alicyclic acrylic resin. Polyolefin resin includes ordinarypolyolefin (such as polyethylene, polypropylene or the like) andalicyclic polyolefin.

[0019]FIG. 12 shows a list of optical characteristics of these resins.

[0020] A photoelasticity constant in the list of FIG. 12 can be used todetermine whether double refraction of a lens formed by plastic moldingis large or small. Acrylic resin is problematic because a moistureabsorption is large although double refraction (photoelasticityconstant) is small, and, in particular, a surface accuracy is likely todeteriorate as environment changes. Although PC (polycarbonate) has ahigh refractive index and a small moisture absorption, a photoelasticityconstant thereof is very large and thereby double refraction is likelyto develop, and wavefront aberration of a light flux transmitted therebyis likely to deteriorate.

[0021] Polyolefin resin has a small moisture absorption and a superiordouble refraction character. Therefore, recently, it is intended thatpolyolefin resin is used as a material of an optical scanning lens.

[0022] However, polyolefin resin has a relatively large mold shrinkagecoefficient in comparison to other plastic materials, molding issomewhat difficult, and a refractive-index distribution is likely todevelop unless molding conditions such as molding pressure, moldingtemperature and so forth are made to be the optimum ones.

SUMMARY OF THE INVENTION

[0023] An object of the present invention is to provide an opticalscanning lens, a refractive index distribution of which is reduced to alevel in which no problem occurs in optical characteristics, and toprovide an optical scanning device using the optical scanning lens andan image forming apparatus using the optical scanning device.

[0024] An optical scanning lens according to the present invention is‘an optical scanning lens used in a scanning and image forming opticalsystem which gathers a light flux deflected by a light deflector in thevicinity of a surface to be scanned’.

[0025] As described above, ‘a scanning and image forming optical system’is an optical system which gathers a light flux deflected by a lightdeflector in the vicinity of a surface to be scanned, and, may consistof a single lens, may consist of a plurality of single lenses, or mayconsist of a combination of one or a plurality of single lens(es) and aspecular surface (concave surface or convex surface) having a functionof forming an image.

[0026] ‘An optical scanning lens’ is a lens used as a component of ascanning and image forming optical system, and one or a plurality ofsingle lens(es) thereof is (are) arranged in the scanning and imageforming optical system. When a scanning and image forming optical systemconsists of a single lens, the optical scanning lens itself is thescanning and image forming optical system.

[0027] An optical scanning lens is formed by ‘plastic molding ofpolyolefin resin’.

[0028] According to the present invention, the following condition issatisfied

0<|Δn(x)−min[Δn(x)]|<34×10⁻⁵  (A)

[0029] where Δn(x) denotes a refractive-index distribution existinginside the lens, in a range which the light flux passes through, in thelens, and min[Δn(x)] denotes the minimum value of the Δn(x).

[0030] The above-mentioned ‘range which the light flux passes through,in the lens’ is a range which a light flux deflected by a lightdeflector passes through the optical scanning lens when being deflected.

[0031] According to another aspect of the present invention, thefollowing condition is satisfied

0<|Δn|<8.5×10⁻⁵  (B)

[0032] where, when Δn(x) denotes a refractive-index distributionexisting inside the lens, in a range between approximately ±1 mm from acenter of the light flux, in a range which the light flux passesthrough, in the lens, Δn denotes a coefficient of second order in‘second-order least-square approximation’ of the Δn(x).

[0033] According to another aspect of the present invention, thefollowing condition is satisfied

0<|Δn(x)−min[Δn(x)]|<34×10⁻⁵  (A)

[0034] where Δn(x) denotes a refractive-index distribution existinginside the lens, in a range which the light flux passes through, in thelens, and min[Δn(x)] denotes the minimum value of the Δn(x), and, also,

[0035] the following condition is satisfied

0<|Δn|<8.5×10⁻⁵  (B)

[0036] where, when Δn(x) denotes a refractive-index distributionexisting inside the lens, in a range between approximately ±1 mm from acenter of the light flux, in a range which the light flux passesthrough, in the lens, Δn denotes a coefficient of second order insecond-order least-square approximation of the Δn(x).

[0037] According to another aspect of the present invention, thefollowing condition is satisfied

0.4×10⁻⁵ <|Δn(x)−min[Δn(x)]|<16×10⁻⁵  (C)

[0038] where Δn(x) denotes a refractive-index distribution existinginside the lens, in a range which the light flux passes through, in thelens, and min[Δn(x)] denotes the minimum value of the Δn(x).

[0039] According to another aspect of the present invention, thefollowing condition is satisfied

0.1×10⁻⁵ <|Δn|<4.0×10⁻⁵  (D)

[0040] where, when Δn(x) denotes a refractive-index distributionexisting inside the lens, in a range between approximately ±1 mm from acenter of the light flux, in a range which the light flux passesthrough, in the lens, Δn denotes a coefficient of second order insecond-order least-square approximation of the Δn(x)

[0041] According to another aspect of the present invention, thefollowing condition is satisfied

0.4×10⁻⁵ <|Δn(x)−min[Δn(x)]|<16×10⁻⁵  (C)

[0042] where Δn(x) denotes a refractive-index distribution existinginside the lens, in a range which the light flux passes through, in thelens, and min[Δn(x)] denotes the minimum value of the Δn(x), and, also,the following condition is satisfied

0.1×10⁻⁵ <|Δn|<4.0×10⁻⁵  (D)

[0043] where, when Δn(x) denotes a refractive-index distributionexisting inside the lens, in a range between approximately ±1 mm from acenter of the light flux, in a range which the light flux passesthrough, in the lens, Δn denotes a coefficient of second order insecond-order least-square approximation of the Δn(x).

[0044] In each aspect of the present invention, when the scanning andimage forming optical system includes a plurality of single lenses, itis possible that the scanning and image forming optical system mayinclude a lens(es) made of PC and/or acrylic resin, a glass lens(es)and/or the like, as a lens(es) other than the optical scanning lens ofthe plurality of single lenses.

[0045] An optical scanning device according to the present invention is‘an optical scanning device which deflects a light flux from a lightsource, gathers the deflected light flux on a surface to be scanned as abeam spot by a scanning and image forming optical system, and performsoptical scanning of the surface to be scanned’.

[0046] As ‘a light source’, various types of well-known ones can beused. In particular, a semiconductor laser is preferable to be used as alight source.

[0047] An optical scanning device according to the present invention ischaracterized in that any optical scanning lens according to the presentinvention is mounted as an optical scanning lens used in a scanning andimage forming optical system.

[0048] It is possible that, in any optical scanning device, a lightdeflector which deflects a light flux from the light source is providedand the light deflector ‘has a deflection reflecting surface anddeflects the light flux at a uniform angular velocity’, and the opticalscanning lens ‘has a function of causing the scanning of the surface tobe scanned to be performed at a uniform velocity’.

[0049] As the above-mentioned ‘light deflector’, it is preferable to usea rotational polygonal (multi-surface) mirror, a rotational dihedral(bi-surface) mirror, or a rotational mono-surface mirror.

[0050] It is possible that, in the optical scanning device, an image isformed from the light flux from the light source in the vicinity of thedeflection reflecting surface of the light deflector, the image beinglike approximately a line long in main scanning directions. For example,it is possible that a light flux from the light source is transformedinto a light-flux form (any form of a parallel light flux, a convergentlight flux and a divergent light flux is possible) suitable for asubsequent optical system by a coupling lens, and, from the thus-coupledlight flux, a line image long in main scanning directions is formed inthe vicinity of the deflection reflecting surface of the light deflectorby a line-image forming optical system such as a cylinder lens. Thereby,it is possible to correct a surface inclination of the light deflector.

[0051] An image forming apparatus according to the present invention is‘an image forming apparatus which performs optical scanning of aphotosensitive surface of an image carrying body and thereby forms alatent image thereon, develops the latent image and thereby visualizesit’.

[0052] In an image forming apparatus according to the present invention,any optical scanning device according to the present invention ismounted as an optical scanning device which performs the opticalscanning the photosensitive surface of the image carrying body as thesurface to be scanned.

[0053] As ‘an image carrying body’, for example, a silver film for anoriginal plate can be used. In this case, a printed image can beobtained as a result of development and fixing of a silver-filmphotographic process being performed on a formed latent image. An imageforming apparatus in this case is ‘a digital plate making machine’.

[0054] It is possible that, the image forming apparatus is ‘an imageforming apparatus in which the image carrying body is a photoconductivephotosensitive body, after the photosensitive body being chargeduniformly, an electrostatic latent image being formed thereon by theoptical scanning, the thus-formed electrostatic latent image beingdeveloped so that a toner image is obtained, and the thus-obtained tonerimage being transferred and fixed onto a sheet-like recording medium’.Thereby, a printed image is obtained. In this case, the image formingapparatus is ‘a digital copier, an optical printer, a laser plotter, afacsimile apparatus or the like’. As the above-mentioned sheet-likerecording medium, transfer paper, a plastic sheet for an overheadprojector, or the like can be used. A transfer of a toner image onto asheet-like recording medium may be a transfer of a toner image from aphotosensitive body to a recording medium directly, or may be a transfervia an intermediate transfer medium such as an intermediate transferbelt.

[0055] According to the present invention, it is possible to achievenovel optical scanning lens, optical scanning device and image formingapparatus.

[0056] An optical scanning lens according to the present invention ismade of polyolefin resin which is superior in a moisture-absorptionproperty and a double-refraction property, and has an internalrefractive-index distribution controlled effectively, thereby being notlikely to be affected by changes in environmental conditions such astemperature, humidity and so forth.

[0057] Further, an optical scanning device according to the presentinvention uses the above-mentioned optical scanning lens, and, thereby,it is possible to achieve an optical scanning device which is not likelyto be affected by environmental fluctuation and is always satisfactory.

[0058] Furthermore, an image forming apparatus according to the presentinvention uses the above-mentioned optical scanning device, and,thereby, it is possible to achieve an image forming apparatus which isnot likely to be affected by environmental fluctuation and is alwayssatisfactory.

[0059] Other objects and further features of the present invention willbecome more apparent from the following detailed description when readin conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0060]FIG. 1 illustrates one embodiment of an optical scanning deviceaccording to the present invention;

[0061]FIGS. 2A through 2E illustrate a refractive-index distributioninside an optical scanning lens;

[0062]FIG. 3 illustrates a change in an image-forming function due to arefractive-index distribution inside an optical scanning lens;

[0063]FIG. 4 illustrates an increase in a beam-spot diameter (beamthickening) due to defocus;

[0064]FIG. 5 illustrates a method of measuring a refractive-indexdistribution inside an optical scanning lens;

[0065]FIG. 6 shows a refractive-index distribution in a sample S1 for anoptical scanning lens;

[0066]FIG. 7 shows a refractive-index distribution in a sample S2 for anoptical scanning lens;

[0067]FIG. 8 shows a refractive-index distribution in a sample S3 for anoptical scanning lens;

[0068]FIG. 9 shows a refractive-index distribution in a sample S4 for anoptical scanning lens;

[0069]FIG. 10 shows a refractive-index distribution in a sample S5 foran optical scanning lens;

[0070]FIG. 11 illustrates one embodiment of an image forming apparatusaccording to the present invention; and

[0071]FIG. 12 shows optical characteristics of various resins.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0072] First, a refractive-index distribution will now be describedsupplementarily.

[0073] A refractive-index distribution Δn(x) is defined as one obtainedas a result of values of ‘a two dimensional absolute refractive index’in a ‘x-y section’ parallel to an optical axis and to sub-scanningdirections of an optical scanning lens (30) shown in FIG. 2C beingaveraged in y-axis directions, and being expressed as a one dimensionalrelative refractive index with respect to x-axis directions (see FIG.2E).

[0074] ‘A range, which a light flux passes through, of a lens’, is, ‘arange, which a light flux deflected by a light deflector passes throughwhen being deflected, of an optical scanning lens’ . In details, withrespect to main scanning directions, ‘a range, which a light flux passesthrough and which corresponds to an effective writing width of a surfaceto be scanned, of a lens’, is a range, which a deflected light fluxpasses through, in the lens. With respect to sub-scanning directions, itis preferable that ‘a range, which a light flux passes through, of alens’, is ‘one on the order of between ±2 nm in consideration of changein an angle at which a light flux emitted from a light source and/orsurface inclination of a light deflector’.

[0075] As shown in FIG. 2C, it is assumed that a direction parallel toan optical axis is a y direction and a direction parallel tosub-scanning directions is a x direction, and, although not shown inFIGS. 2A through 2E, it is assumed that a direction parallel to mainscanning directions is a z direction.

[0076] An absolute refractive index n in a plane, which is perpendicularto the z direction at an arbitrary position in the main scanningdirections, is expressed by n(x, y). An average of absolute refractiveindexes n(x, y) in the y direction parallel to the optical axis iscalculated by

[∫n(x, y)dy]/d(x)

[0077] where d(x) denotes a thickness of the lens in the optical-axisdirections with respect to the x direction. The integration is performedthrough the thickness of the lens d(x).

[0078] ‘An appropriate reference value’ is set for the result of theabove-mentioned calculation, and a difference between this set value andthe result of the calculation is calculated. Thereby, theabove-mentioned ‘refractive-index distribution Δn(x) obtained as aresult of values of a two dimensional absolute refractive index in a x-ysection parallel to the optical axis and to the sub-scanning directionsof the optical scanning lens being averaged in the y-axis directions,and being expressed as a one dimensional relative refractive index withrespect to the x-axis directions’ is obtained. FIG. 2E shows thethus-obtained Δn(x).

[0079] Δn(x) in the following conditional expression (C) is thethus-obtained Δn(x):

0.4×10⁻⁵ <|Δn(x)−min[Δn(x)]|<16×10⁻⁵

[0080] ‘A method of obtaining a refractive-index distribution Δn(x)’ foran actual optical scanning lens will now be described.

[0081]FIG. 5 illustrates an apparatus of measuring a refractive-indexdistribution using a Mach-Zehnder interferometer as a basic arrangementthereof.

[0082] A laser light flux which is coherence light is emitted by a laserlight source 1, is transformed into a parallel light flux as a result ofa diameter thereof being enlarged by a beam expander 3, and is incidenton a beam splitter 5. The beam splitter 5 splits the incident laserlight flux into two light fluxes. Specifically, the incident laser lightflux is split by the beam splitter 5 into one laser light flux which isobtained as a result of being bent at a right angle by the beam splitter5 and is of a reference wave ‘a’, and another laser light flux which isobtained as a result of being transmitted straightly by the beamsplitter 5, being reflected by a reflective mirror 9 and beingtransmitted by a phase object as an object to be examined A and is of awave to be examined ‘b’. The beam splitter 5 splits the incident lightflux in a manner such that a ratio of intensities of the reference wave‘a’ and wave to be examined ‘b’ be approximately ‘1:1’.

[0083] A reflective mirror 7 is supported by an electricity-movementconverting device 19 formed of a piezoelectric device or the like, andis arranged in a manner such that a length of light path of thereference wave ‘a’ can be changed in the order of wave length for apurpose of performing analysis of interference fringes in accordancewith a phase shifting method.

[0084] The reference wave ‘a’ is reflected by the reflective mirror 7and reaches a beam splitter 11. The wave to be examined ‘b’ is reflectedby the reflective mirror 9, is transmitted by the object to be examinedA, and reaches the beam splitter 11. The beam splitter 11 joins thereference wave ‘a’ and wave to be examined ‘b’ together into a joinedlight flux, and splits the joined light flux into two light fluxes. Theelectricity-movement converting device 19 is adjusted so that ‘a phasedifference of mπ/2’ be obtained in length of light path between thereference wave ‘a’ and wave to be examined ‘b’ to be joined together,where ‘m’ is an integer. One split light flux of the joined light fluxsplit by the beam splitter 11 is incident on an image forming lens 13,and, thereby, an image of interference fringes (of the reference wave‘a’ and wave to be examined ‘b’) is formed on an image pickup surface ofan interference-fringe detector 15. As the interference-fringe detector15, a linear CCD, or an array-like sensor is used. The other split lightflux of the joined light flux split by the beam splitter 11 is incidenton an image pickup surface of a CCD camera for monitoring 23, and,thereby, an image of the interference fringes is formed thereon, throughan image forming lens 31.

[0085] A refractive index of the object to be examined A is considerablydifferent from that of the air, and, unless an incident side and anemitting side of the object to be examined A are parallel to oneanother, the wave to be examined ‘b’ transmitted by the object to beexamined A converges/diverges irregularly depending on a shape of theobject to be examined A. In order to cause an image of interferencefringes to be formed on the image pickup surface of theinterference-fringe detector 15, the wave to be examined ‘b’ should be‘an approximately parallel light flux’. The following arrangement ismade in order to cause the wave to be examined ‘b’ having beentransmitted by the object to be examined A to be an approximatelyparallel light flux regardless of a shape of the object to be examinedA.

[0086] That is, the object to be examined A is set inside a cell 21provided on a light path of the wave to be examined ‘b’, and the cell 21is filled with a test liquid B ‘made up so that a refractive indexthereof is approximately equal to a refractive index of the object to beexamined A’. Two ends of the cell 21, that is an incident window 25 andan emitting window 27 for the wave to be examined ‘b’ are parallel toone another, and optical flats 28 and 29 each having high surfaceaccuracy are attached thereto, and the cell 21 is sealed for preventingthe liquid inside from leaking.

[0087] The cell 21 filled with the object to be examined A and testliquid B is an object, a refractive index of which is uniform throughthe entirety thereof, and an incident surface and an emitting surface ofwhich are parallel to one another. Accordingly, the wave to be examined‘b’ transmitted by the cell 21 is emitted therefrom as being anapproximately parallel light flux. When a refractive-index distributioninside the object to be examined A is non-uniform, a wave surface of thewave to be examined ‘b’ emitted from the cell 21 has ‘a curved-surfaceshape depending on the refractive-index distribution’. Interferencefringes, an image of which is formed on the image pickup surface of theinterference-fringe detector 15, develop due to interference between thewave to be examined ‘b’ of the above-mentioned curved-surface shape andthe reference wave ‘a’ which is a plane wave. The curved-surface shapeof the wave to be examined ‘b’ can be measured by well-known analysis ofinterference fringes.

[0088] An image of interference fringes is detected by theinterference-fringe detector 15, undergoes photoelectric conversion soas to become an electric image signal, is converted into a digitalsignal by an A-D converter 33, and is input to a calculation device 17.

[0089] The calculation device 17 includes a transmitted wave surfacemeasuring unit 35 which measures and calculates a transmitted wavesurface (a shape of wave surface of the wave to be examined ‘b’) byanalysis of interference fringes. Specifically, the calculation device17 is a personal computer or the like which ‘has a CPU and performsvarious calculation processes in accordance with programs stored in ahard disk drive or the like’.

[0090] A refractive-index distribution of an optical scanning lens asthe object to be examined A is measured as follows.

[0091] The optical scanning lens as the object to be measured A is setin the cell 21, coherent light from the laser light source 1 is incidenton the optical scanning lens, and, as described above, an image ofinterference fringes is formed on the interference-fringe detector 15.An image signal of the image of interference fringes output by theinterference-fringe detector 15 is input to the calculation device 17,the transmitted wave surface measuring unit 35 in the calculating device17 performs ‘analysis of interference fringes’, and, thus, a transmittedwave surface WF(x) is measured. The apparatus shown in FIG. 5 isarranged so that a direction of a linear CCD of the interference-fringedetector 15 corresponds to the x direction (sub-scanning directions)described above with respect to the optical scanning lens.

[0092] A thickness d(x) in optical-axis directions of the opticalscanning lens as the object to be examined A is obtained previously fromdesign data of the optical scanning lens or measured data thereof by ageneral-purpose measuring apparatus.

[0093] As mentioned above, based on an output of the linear CCD of theinference-fringe detector 15, the transmitted wave surface WF(x) ismeasured by the transmitted wave surface measuring unit 35. Then, anarbitrary position on the linear CCD is determined to be a position of‘x=0’ and a reference transmitted wave surface WF(0) is obtained, and,then, Δn(x) is calculated by the following equation:

Δn(x)={WF(x)−WF(0)}·λ/d(x)

[0094] Thus, a refractive-index distribution Δn(x) can be calculated foran arbitrary measurement section. A refractive-index distribution inmain scanning directions is such that variation is small in comparisonto that in sub-scanning directions. Therefore, by measuring for severalspecific sections (of middle portion, peripheral portion and so forth),it is possible to grasp a refractive-index distribution of the entiretyof an optical scanning lens. It is possible to use a refractive-indexdistribution measured for one section of a middle portion or the like asa representative one of an overall refractive-index distribution, forthose such as mass-produced ones for which mold conditions are stable. Achange of a measurement section can be performed by changing a positionrelationship between the linear CCD and a lens to be examined to be thatsuch that the lens to be examined is moved in z directions relative tothe linear CCD.

[0095] This measuring method is disclosed by Japanese Laid-Open PatentApplication No. 11-044641, the entire contents of which are herebyincorporated by reference.

[0096] In the above-described method, Δn(x) is calculated from ‘anoptical-axis directional thickness directionally added-up transmittedwave surface’. Accordingly, although ‘a refractive-index distribution inoptical-axis directions’ such as that shown in FIG. 2D cannot beobtained, average data Δn(x) obtained as a result of it being added upin optical-axis directions is sufficient to grasp opticalcharacteristics of an optical scanning lens. Further, because Δn(x) isof one dimension, this can be easily managed as an evaluation itemadvantageously.

[0097] Δn(x) in the above equation is a function of only ‘x’. However,it is possible to perform two-dimensional measurement.

[0098] Δn(x) calculated as mentioned above can be expanded by apolynominal approximation as follows:

Δn(x)≈n0+n1·x+n2·x ² +n3·x ³  (1)

[0099] (The symbol ‘≈’ signifies ‘is approximately equal to’.)

[0100] Then, by obtaining respective coefficients n0, n1, n2, . . . , nm(coefficient of a term of a highest m-th order), it is possible toobtain a refractive-index distribution at a position of a coordinate ‘x’on an x-axis directly. Although the number of order of theabove-mentioned polynominal is arbitrary, the second order is selected,for example, and the following equation is used.

Δn(x)=n ₀ +n1·x+Δn·x ²+δ(x)  (2)

[0101] In the right side of this equation, ‘a coefficient of secondorder Δn’ affects optical characteristics largely. Because a coefficientof first order n₀ has a small optical influence, it is possible toneglect the coefficient. δ (x) is a residual due to second-orderapproximation and is a slight amount. Accordingly, the followingexpression can be obtained.

Δn(x)≈n ₀ +Δn·x ²  (3)

[0102] In the above expression (3), Δn is determined by a least squaresmethod.

[0103] In the above expression (3), the coefficient of second order Δnfunctions as ‘a lens power’. Because a diameter of a light flux passingthrough an optical scanning lens is on the order of 1 mm in general, arange of ‘x’ when Δn is calculated is determined to be one between ±1mm, here.

[0104] Influence which is exerted on a lens function by the coefficientof second order Δn will now be described making reference to FIG. 3. InFIG. 3, points E and F are front and rear principal points of a lens LN,respectively, a point Q is an image point of an object point P. A lengthf is a design focal length of the lens LN. Lengths S and S′ are a designobject distance and a design image distance, respectively.

[0105] As described above, a refractive-index distribution can beregarded as ‘functioning as a lens’. Therefore, when considering ‘a lensequivalent to a refractive-index distribution’, it is possible toexpress a relationship between a focal length f′ of the equivalent lens,Δn, and a lens thickness t, by the following expression.

f′≈1/(2·Δn·t)  (4)

[0106] (When an optical scanning lens is a compound lens consisting of aplurality of single lenses, a lens thickness t in the above expression(4) is ‘the sum in thickness of respective single lenses of the opticalscanning lens’.)

[0107] A focal length of a lens having a refractive-index distributionis a focal length of a compound system of a lens having a design focallength f and an equivalent lens having a focal length f′, and a changein focal length Δf can be expressed by approximation as follows.

Δf≈f ² /f′  (5)

[0108] A shift in position of image formation ΔS′ due to arefractive-index distribution can be expressed using the following thinlens's paraxial image-formation formula:

(1/S′=1/S+1/f)

[0109] as follows. $\begin{matrix}\begin{matrix}{{\Delta \quad S^{\prime}} \approx {{\left\{ {S/\left( {S + f} \right)} \right\}^{2} \cdot \Delta}\quad f}} \\{= {\left\{ {f \cdot {S/\left( {S + f} \right)}} \right\}^{2}/f^{\prime}}} \\{= {\left( S^{\prime} \right)^{2} \cdot \left( {{2 \cdot \Delta}\quad {n \cdot t}} \right)}}\end{matrix} & (6)\end{matrix}$

[0110] When L denotes a distance between a deflection reflecting surfaceof a light deflector and a surface to be scanned as shown in FIG. 1 andβ denotes a lateral magnification of an optical scanning lens 30, theabove expression (6) can be expressed by approximation as follows.

ΔS′≈{β/(β−1)·L} ²·(2·Δn·t)  (7)

[0111] By using the above expression (7), an amount of defocus ΔS′ canbe obtained from the above-mentioned ‘Δn’ of an optical scanning lens bycalculation.

[0112] When ‘an allowance of focal depth’ is defined as an allowance ofdefocus in the range between ±10% from a beam-spot diameter (a diameterat which a beam intensity is 1/e² of a peak value), a theoreticalallowance of focal depth w is obtained by the following expression (8)using a beam-spot diameter d and a wavelength λ.

w≈1.487×d ²/λ  (8)

[0113] When it is possible to control a shift in position of imageformation ΔS′ in the range of this allowance of focal depth w, it ispossible to obtain a stable beam-spot diameter on a surface to bescanned. That is, an optical scanning lens should be made as a lenswhich satisfies the following condition.

w≧Δs′  (9)

[0114] By using the above-expression (9), it is possible to determine ‘amagnitude of Δn’ so that a beam-spot diameter can be controlled in anallowable range. Because a refractive-index distribution is determineddepending on a degree of a magnitude of Δn, it is possible to achieve asatisfactory beam-spot diameter by controlling a refractive-indexdistribution Δn(x) within a predetermined range.

[0115] An embodiment of the present invention will now be describedregarding an optical scanning device shown in FIG. 1 as the embodimentof the present invention. An optical scanning lens 30 is ‘made to bemost suitable to conditions in which the optical scanning device isused’ in accordance with a design.

[0116] In the optical scanning device shown in FIG. 1, assuming that atarget beam-spot diameter d is such that d=70 (μm) and a wavelength λ ofa semiconductor laser (as a light source) is such that λ=400 (nm), anallowance of focal depth w is such that w=18.2 (mm) by the expression(8). When the optical scanning lens 30 is used under conditions suchthat a length of optical path L is such that L=200 (mm), a lateralmagnification β is such that β=−1.0, a lens thickness t is such thatt=10 (mm), and a beam effective diameter is ±2 mm, it can be determinedthat Δn should be equal to or less than 9.1×10⁻⁵, as a result ofcalculating backward from the allowance by the expression (9).

[0117] As another case, assuming that a target beam-spot diameter d issuch that d=90 (μm) and a wavelength λ of a semiconductor laser is suchthat λ=650 (nm), an allowance of focal depth w is such that w=18.5 (mm)by the expression (8). When the optical scanning lens 30 is used underconditions such that a length of optical path L is such that L=200 (mm),a lateral magnification β is such that β=−0.5, a lens thickness t issuch that t=20 (mm), and a beam effective diameter is ±2 mm, it can bedetermined that An should be equal to or less than 10.4×10⁻⁵ so that theallowance is satisfied.

[0118] A shape of the lens 30 (a radius of curvature, a thickness and arefractive index) and a mounting accuracy actually deviate from designvalues due to a manufacturing process and so forth. It is preferablethat an allowance of ‘a shift in lens shape’ be within the range of 10to 20% of a value corresponding to an allowance of focal depth.

[0119] Accordingly, a coefficient of second order Δn of arefractive-index distribution should satisfy the following condition.

0<|Δn|<8.5×10⁻⁵  (B)

[0120] When a refractive-index distribution Δn(x) denotes non-uniformityof refractive index existing inside the lens in the range between ±2 mmin sub-scanning directions and min[Δn(x)] denotes the minimum valuethereof, it can be determined that these should satisfy

0<|Δn(x)−min[Δn(x)]|<34×10⁻⁵  (A)

[0121] as a result of values such that Δn=8.5×10⁻⁵ and x=2 beingsubstituted for Δn and x in the following expression

Δn(x)≈n₀ +Δn·x ²  (3)

[0122] so that ‘a shift in lens shape’ be within an allowance. When|Δn(x)−min[Δn(x)]|≧34×10⁻⁵, optical characteristics deteriorateregardless of shape and size of a lens.

[0123] In view of practical use, it is preferable that the followingconditions are satisfied.

0.1×10⁻⁵ <|Δn|<4.0×10⁻⁵  (D)

0.4×10⁻⁵ <|Δn(x)−min[Δn(x)]|<16×10⁻⁵  (C)

[0124] When |Δn| exceeds the upper limit 4.0×10⁻⁵ and increases, it isnecessary to limit a wavelength λ to be used and/or decreases an opticalmagnification |β|, and restrictions on an optical design become strict.On the other hand, when |Δn| exceeds the lower limit 0.1×10⁻⁵ anddecreases, not only a measurement error cannot be ignored, but also acooling time required for molding increases, manufacturing efficiencydeteriorates, and cost increases.

[0125] As a result of a refractive-index distribution inside an opticalscanning lens being able to be measured non-destructively by such amethod as that described above, it is possible to determine whether ornot optical characteristics of an optical scanning lens made ofpolyolefin resin is satisfactory without actually performing measurementof the optical characteristics.

[0126] In the embodiment shown in FIG. 1, a length of light path Lbetween a light deflector 20 and a surface to be scanned 40 isdetermined such that L=200 (mm), an optical scanning lens 30 is designedto be an optimum one under conditions such that a lens thickness tthereof is such that t=10 (mm) and a lateral magnification β thereof issuch that β=−1.0.

[0127] Samples S1 through S5 were made by plastic molding usingpolyolefin resin (ordinary polyolefin) in five different mold conditionsfor the above-mentioned optical scanning lens.

[0128] Results of measurements of refractive-index distributions Δn(x)for these samples are shown in FIGS. 6 through 10 . In each of FIGS. 6through 10, a refractive-index distribution Δn(x) of a vertical axis isindicated assuming that a reference value of Δn(x) is 0, ‘short-lengthdirection’ indicated for a horizontal axis is sub-scanning directions,and, is the above-mentioned x direction, and the range between ±2 mm ofupper and lower limits of the horizontal axis is ‘a range in thesub-scanning directions which a light flux passes through’. FIGS. 7 and9 show three types of refractive-index distributions Δn(x) for different‘lens heights’, respectively. A ‘height’ in the figures indicates aposition of plane in main scanning directions, in which planemeasurement of Δn(x) is made, assuming that the optical-axis position is0. That is, in FIGS. 7 and 9, the three types of refractive-indexdistributions Δn(x) are refractive-index distributions in respectivepositions in the main scanning directions such that z=0, 25, and 50 (mm)assuming that the optical-axis position is such that z=0.

[0129] The above-mentioned ‘|Δn(x)−min[Δn(x)]|’ and a coefficient ofsecond order Δn in a quadratic expression obtained as a result of Δn(x)being expanded in the range between ±1 mm, within a range in the lenswhich a light flux passes through (within the range between ±50 mm inthe main scanning directions and ±2 mm in the sub-scanning directions),of the samples S1 through S5, are as follows:

[0130] For a sample S1,

|Δn(x)−min[Δn(x)]|≦53.9×10⁻⁵,

Δn=10.3×10⁻⁵[1/mm²]

[0131] For a sample S2,

|Δn(x)−min[Δn(x)]|≦2.1×10⁻⁵,

Δn=0.5×10⁻⁵[1/mm²]

[0132] For a sample S3,

|Δn(x)−min[Δn(x)]|≦29.7×10⁻⁵,

Δn=8.3×10⁻⁵[1/mm²]

[0133] For a sample S4,

|Δn(x)−min[Δn(x)]|≦13.8×10⁻⁵,

Δn=3.8×10⁻⁵[1/mm²]

[0134] For a sample S5,

|Δn(x)−min[Δn(x)]|≦0.47×10⁻⁵,

Δn=−0.2×10⁻⁵[1/mm²]

[0135] As described above, the optical scanning lens 30 is designed toan optimum one in the conditions such that the length of light pathL=200 (mm), the lateral magnification β=−1.0, and the lens thicknesst=10 (mm). An amount of defocus developing due to a refractive-indexdistribution inside the lens is obtained by the expression (4) asfollows: 20.6 mm for the sample S1, 1.0 mm for the sample S2, 16.6 mmfor the sample S3, 7.6 mm for the sample S4 and −0.4 mm for the sampleS5. When these are compared with the above-described allowance of focaldepth w (w=18.2 (mm) when a target beam-spot diameter d=70 (μm) and awave length of the semiconductor laser λ=400 (nm); w=18.5 (mm) when atarget beam-spot diameter d=90 (μm) and a wave length of thesemiconductor laser λ=650 (nm)), for the sample S1, because the amountof defocus is larger than the allowance of focal depth, the sample S1 isrejected as an optical scanning lens. However, for each of the samplesS2 through S5, because the amount of defocus is controlled within theallowance of focal depth, these samples can be used as optical scanninglenses. It is noted that results of actually measuring allowances offocal depth by measuring beam diameters were similar to the abovecalculation results, and, thereby, correctness of the calculationresults was proved.

[0136] When comparison is made only for the refractive-indexdistributions Δn(x), the sample S5 is most satisfactory. However,manufacturing costs of the respective samples differ from each other dueto differences in mold temperature, holding pressure, mold time and soforth. Accordingly, which one is the best should be determined as aresult of these factors being considered synthetically.

[0137] Practical preferable examples of a scanning optical system andcalculation results of allowances of focal depth w and coefficients Δntherefor are shown below.

[0138] {circle over (1)} An optical system using an inexpensive laserhaving a long wavelength:

[0139] w=15.4 (mm) and Δn=3.8×10⁻⁵ in a case where d=90 (μm), λ=780(nm), L=175 (mm), β=−2.3, and t=13.5 (mm).

[0140] Accordingly, the samples S2, S4 and S5 can be used as opticalscanning lenses.

[0141] {circle over (2)} An optical system in which a target beamdiameter is small:

[0142] w=6.9 (mm) and Δn=1.4×10⁻⁵ in a case where d=55 (μm), λ=650 (nm),L=226 (mm), β=−1.1, and t=18 (mm).

[0143] Accordingly, the samples S2 and S5 can be used as opticalscanning lenses.

[0144] {circle over (3)} An optical system in which a scanning width iswide and it is necessary that a distance L between a deflectionreflecting surface and a photosensitive body is long:

[0145] w=9.6 (mm) and Δn=0.45×10⁻⁵ in a case where d=65 (μm), λ=655(nm), L=307 (mm), β=−1.5, and t=31.4 (mm).

[0146] Accordingly, the sample S5 can be used as an optical scanninglens.

[0147] {circle over (4)} An optical system in which a target beamdiameter is very small, also a scanning width is wide and it isnecessary that a distance L between a deflection reflecting surface anda photosensitive body is long:

[0148] w=2.1 (mm) and Δn=0.11×10⁻⁵ in a case where d=30 (μm), λ=650(nm), L=300 (mm), β=−1.1, and t=39 (mm).

[0149] Accordingly, no sample can be used as an optical scanning lens.In this case, it is necessary to form a plastic-molded lens having arefractive-index distribution smaller than that of the sample S5. When acertain degree of restriction conditions should thus be satisfied in anoptical design, it is preferable that the following conditions aresatisfied.

0.1×10⁻⁵ <|Δn|<4.0×10⁻⁵  (D)

0.4×10⁻⁵ <|Δn(x)−min[Δn(x)]|<16×10⁻⁵  (C)

[0150] However, these conditions (C) and (D) are not limited for theabove-mentioned optical systems {circle over (1)} through {circle over(4)}.

[0151] The above-mentioned expressions (A), (B), (C) and (D) arenormalized for a lens thickness. Accordingly, these are applied for eachsingle lens when an optical scanning lens is a compound lens consistingof a plurality of single lenses.

[0152] An embodiment of an image forming apparatus according to thepresent invention will now be described. FIG. 11 roughly shows a laserprinter in the embodiment of the image forming apparatus according tothe present invention.

[0153] The laser printer 100 has a ‘cylindrical photoconductivephotosensitive body’ as an image carrying body 111. Around the imagecarrying body 111, a charting roller 112 as a charting unit, adeveloping unit 113, a transfer roller 114 and a cleaning unit 115 arearranged. In this embodiment, the charging roller 112 of a contact-typecharging roller which generates less ozone is used as a charting unit.However, it is also possible to use a corona charger utilizing coronadischarging as a charting unit, instead. Further, an optical scanningdevice 117 is provided, which performs ‘exposure by optical scanning bya laser beam LB’ between the charging roller 112 and developing unit113.

[0154] Further, as shown in FIG. 11, a fixing unit 116, a cassette 118,a pair of registration rollers 119, a paper feeding roller 120, aconveyance printer 121, a pair of paper ejecting rollers 122, and a tray123 are provided.

[0155] When a printed image is formed, the image carrying body 111 whichis the photoconductive photosensitive body is rotated at a uniformvelocity, a surface thereof is charged uniformly by the charging roller112, and a electrostatic latent image is formed thereon by exposure byoptical writing by a laser beam performed by the optical scanning device117. The thus-formed electrostatic latent image is a so-called ‘negativelatent image’ and in which an image portion is exposed.

[0156] The electrostatic latent image is developed by the developingunit 113 so that a toner image (positive image) is formed on the imagecarrying body 111. The cassette 118 containing transfer paper isdetachable from a body of the laser printer 100, and, in a condition inwhich the cassette 118 is attached to the body as shown in the figure, atop sheet of the transfer paper contained thereby is fed by the paperfeeding roller 120. The thus-fed transfer-paper sheet is taken by thepair of the registration rollers 119 at the front end thereof. The pairof registration rollers 119 feed the transfer-paper sheet to thetransfer roller 114 at a time at which the toner image on the imagecarrying body 111 moves to the transfer roller 114. The thus-fedtransfer-paper sheet is laid on the toner image at the transfer roller114 and, by a function of the transfer roller 114, the toner image iselectrostatically transferred onto the transfer-paper sheet. Thetransfer-paper sheet having the toner image transferred thereonto hasthe toner image fixed thereonto by the fixing unit 116, then, passesthrough the conveyance printer 121, and is ejected onto the tray 123 bythe pair of paper ejecting rollers 122.

[0157] After the toner image is transferred to the transfer-paper sheet,the surface of the image carrying body 111 is cleaned by the cleaningunit 115, and, thus, residual toner, paper powder and so forth areremoved therefrom.

[0158] As ‘the optical scanning device 117’, that described above inaccordance with FIG. 1 is used, and, as an optical scanning lens 30thereof, that formed by plastic molding of polyolefin resin describedabove and satisfying the above-mentioned condition(s) (A) and/or (B), orcondition(s) (C) and/or (D) is mounted.

[0159] Further, the present invention is not limited to theabove-described embodiments, and variations and modifications may bemade without departing from the scope of the present invention.

[0160] The present application is based on Japanese priority applicationNo. 11-163037, filed on Jun. 9, 1999, the entire contents of which arehereby incorporated by reference.

What is claimed is:
 1. An optical scanning lens which is used in ascanning and image forming optical system which gathers a light fluxdeflected by a light deflector in the vicinity of a surface to bescanned, wherein: said lens is formed by a resin having the followingproperties: photoelasticity constant≦8 (10⁻¹³cm²/dyne); saturationmoisture absorption≦0.5(%); and mold shrinkage coefficient≧20.7(%), andthe following condition is satisfied: 0<|Δn(x)−min[Δn(x)]|<34×10⁻⁵  (A)wherein: Δn(x) denotes a refractive-index distribution existing insidesaid lens, in a range which the light flux passes through, in said lens;and min [Δn(x)] denotes the minimum value of said Δn(x).
 2. An opticalscanning lens which is used in a scanning and image forming opticalsystem which gathers a light flux deflected by a light deflector in thevicinity of a surface to be scanned, wherein: said lens is formed by aresin having the following properties: photoelasticity constant≦8(10⁻¹³cm²/dyne); saturation moisture absorption≦0.5(%); and moldshrinkage coefficient≧0.7(%), and the following condition is satisfied:0<|Δn|<8.5×10⁻⁵  (A) where, when Δn(x) denotes a refractive-indexdistribution existing inside of said lens, in a range betweenapproximately ±1 mm from a center of the light flux, in a range whichthe light flux passes through, in said lens, Δn denotes a quadraticcoefficient in quadratic least-square approximation of said Δn(x). 3.The optical scanning lens as claimed in claim 2, wherein the followingcondition is satisfied 0<|Δn|<8.5×10⁻⁵  (B) where, when Δn(x) denotes arefractive-index distribution existing inside said lens, in a rangebetween approximately ±1 mm from a center of the light flux, in a rangewhich the light flux passes through, in said lens, Δn denotes acoefficient of second order in second-order least-square approximationof said Δn(x).
 4. An optical scanning lens which is used in a scanningand image forming optical system which gathers a light flux deflected bya light deflector in the vicinity of a surface to be scanned, wherein:said lens is formed by a resin having the following properties:photoelasticity constant≦8 (10⁻¹³cm²/dyne); saturation moistureabsorption≦0.5(%); and mold shrinkage coefficient≧0.7(%), and thefollowing condition is satisfied: 0.4×10⁵<|Δn(x)−min[Δn(x)]|<16×10⁻⁵  (A) where: Δn(x) denotes a refractive-indexdistribution existing inside said lens, in a range which the light fluxpasses through, in said lens; and min [Δn(x)] denotes the minimum valueof said Δn(x).
 5. An optical scanning lens which is used in a scanningand image forming optical system which gathers a light flux deflected bya light deflector in the vicinity of a surface to be scanned, wherein:said lens is formed by a resin having the following properties:photoelasticity constant≦8 (10⁻¹³cm²/dyne); saturation moistureabsorption≦0.5(%); and mold shrinkage coefficient≧0.7(%), and thefollowing condition is satisfied: 0.1×10⁻⁵ <|Δn|<4.0×10⁻⁵  (A) where,when Δn(x) denotes a refractive-index distribution existing inside ofsaid lens, in a range between approximately ±1 mm from a center of thelight flux, in a range which the light flux passes through, in saidlens, Δn denotes a quadratic coefficient in quadratic least-squareapproximation of said Δn(x).
 6. The optical scanning lens as claimed inclaim 5, wherein the following condition is satisfied 0.1×10⁻⁵<|Δn|<4.0×10⁻⁵  (B) where, when Δn(x) denotes a refractive-indexdistribution existing inside said lens, in a range between approximately±1 mm from a center of the light flux, in a range which the light fluxpasses through, in said lens, Δn denotes a coefficient of second orderin second-order least-square approximation of said Δn(x).
 7. An opticalscanning device which deflects a light flux from a light source, gathersthe deflected light flux on a surface to be scanned by a scanning andimage forming optical system as a beam spot, and performs opticalscanning of said surface to be scanned, wherein the optical scanninglens as claimed in claim 1 is mounted as an optical scanning lens usedin said scanning and image forming optical system.
 8. An opticalscanning device which deflects a light flux from a light source, gathersthe deflected light flux on a surface to be scanned by a scanning andimage forming optical system as a beam spot, and performs opticalscanning of said surface to be scanned, wherein the optical scanninglens as claimed in claim 2 is mounted as an optical scanning lens usedin said scanning and image forming optical system.
 9. An opticalscanning device which deflects a light flux from a light source, gathersthe deflected light flux on a surface to be scanned by a scanning andimage forming optical system as a beam spot, and performs opticalscanning of said surface to be scanned, wherein the optical scanninglens as claimed in claim 3 is mounted as an optical scanning lens usedin said scanning and image forming optical system.
 10. An opticalscanning device which deflects a light flux from a light source, gathersthe deflected light flux on a surface to be scanned by a scanning andimage forming optical system as a beam spot, and performs opticalscanning of said surface to be scanned, wherein the optical scanninglens as claimed in claim 4 is mounted as an optical scanning lens usedin said scanning and image forming optical system.
 11. An opticalscanning device which deflects a light flux from a light source, gathersthe deflected light flux on a surface to be scanned by a scanning andimage forming optical system as a beam spot, and performs opticalscanning of said surface to be scanned, wherein the optical scanninglens as claimed in claim 5 is mounted as an optical scanning lens usedin said scanning and image forming optical system.
 12. An opticalscanning device which deflects a light flux from a light source, gathersthe deflected light flux on a surface to be scanned by a scanning andimage forming optical system as a beam spot, and performs opticalscanning of said surface to be scanned, wherein the optical scanninglens as claimed in claim 6 is mounted as an optical scanning lens usedin said scanning and image forming optical system.
 13. The opticalscanning device as claimed in claim 7 comprising a light deflector whichdeflects the light flux from the light source, wherein: said lightdeflector has a deflection reflecting surface and deflects the lightflux at a uniform angular velocity; and said optical scanning lens has afunction of causing the scanning of said surface to be scanned to beperformed at a uniform velocity.
 14. The optical scanning device asclaimed in claim 8 comprising a light deflector which deflects the lightflux from the light source, wherein: said light deflector has adeflection reflecting surface and deflects the light flux at a uniformangular velocity; and said optical scanning lens has a function ofcausing the scanning of said surface to be scanned to be performed at auniform velocity.
 15. The optical scanning device as claimed in claim 9comprising a light deflector which deflects the light flux from thelight source, wherein: said light deflector has a deflection reflectingsurface and deflects the light flux at a uniform angular velocity; andsaid optical scanning lens has a function of causing the scanning ofsaid surface to be scanned to be performed at a uniform velocity. 16.The optical scanning device as claimed in claim 10 comprising a lightdeflector which deflects the light flux from the light source, wherein:said light deflector has a deflection reflecting surface and deflectsthe light flux at a uniform angular velocity; and said optical scanninglens has a function of causing the scanning of said surface to bescanned to be performed at a uniform velocity.
 17. The optical scanningdevice as claimed in claim 11 comprising a light deflector whichdeflects the light flux from the light source, wherein: said lightdeflector has a deflection reflecting surface and deflects the lightflux at a uniform angular velocity; and said optical scanning lens has afunction of causing the scanning of said surface to be scanned to beperformed at a uniform velocity.
 18. The optical scanning device asclaimed in claim 12 comprising a light deflector which deflects thelight flux from the light source, wherein: said light deflector has adeflection reflecting surface and deflects the light flux at a uniformangular velocity; and said optical scanning lens has a function ofcausing the scanning of said surface to be scanned to be performed at auniform velocity.
 19. The optical scanning device as claimed in claim 13wherein an image is formed from the light flux from the light source inthe vicinity of the deflection reflecting surface of said lightdeflector, said image being like approximately a line long in mainscanning directions.
 20. The optical scanning device as claimed in claim14 wherein an image is formed from the light flux from the light sourcein the vicinity of the deflection reflecting surface of said lightdeflector, said image being like approximately a line long in mainscanning directions.
 21. The optical scanning device as claimed in claim15 wherein an image is formed from the light flux from the light sourcein the vicinity of the deflection reflecting surface of said lightdeflector, said image being like approximately a line long in mainscanning directions.
 22. The optical scanning device as claimed in claim16 wherein an image is formed from the light flux from the light sourcein the vicinity of the deflection reflecting surface of said lightdeflector, said image being like approximately a line long in mainscanning directions.
 23. The optical scanning device as claimed in claim17 wherein an image is formed from the light flux from the light sourcein the vicinity of the deflection reflecting surface of said lightdeflector, said image being like approximately a line long in mainscanning directions.
 24. The optical scanning device as claimed in claim18 wherein an image is formed from the light flux from the light sourcein the vicinity of the deflection reflecting surface of said lightdeflector, said image being like approximately a line long in mainscanning directions.
 25. An image forming apparatus which performsoptical scanning of a photosensitive surface of an image carrying bodyand thereby forms a latent image thereon, develops the latent image andthereby visualizes it, wherein the optical scanning device as claimed inclaim 7 is mounted as an optical scanning device which performs theoptical scanning of the photosensitive surface of said image carryingbody as the surface to be scanned.
 26. An image forming apparatus whichperforms optical scanning of a photosensitive surface of an imagecarrying body and thereby forms a latent image thereon, develops thelatent image and thereby visualizes it, wherein the optical scanningdevice as claimed in claim 8 is mounted as an optical scanning devicewhich performs the optical scanning of the photosensitive surface ofsaid image carrying body as the surface to be scanned.
 27. An imageforming apparatus which performs optical scanning of a photosensitivesurface of an image carrying body and thereby forms a latent imagethereon, develops the latent image and thereby visualizes it, whereinthe optical scanning device as claimed in claim 9 is mounted as anoptical scanning device which performs the optical scanning of thephotosensitive surface of said image carrying body as the surface to bescanned.
 28. An image forming apparatus which performs optical scanningof a photosensitive surface of an image carrying body and thereby formsa latent image thereon, develops the latent image and thereby visualizesit, wherein the optical scanning device as claimed in claim 10 ismounted as an optical scanning device which performs the opticalscanning of the photosensitive surface of said image carrying body asthe surface to be scanned.
 29. An image forming apparatus which performsoptical scanning of a photosensitive surface of an image carrying bodyand thereby forms a latent image thereon, develops the latent image andthereby visualizes it, wherein the optical scanning device as claimed inclaim 11 is mounted as an optical scanning device which performs theoptical scanning of the photosensitive surface of said image carryingbody as the surface to be scanned.
 30. An image forming apparatus whichperforms optical scanning of a photosensitive surface of an imagecarrying body and thereby forms a latent image thereon, develops thelatent image and thereby visualizes it, wherein the optical scanningdevice as claimed in claim 12 is mounted as an optical scanning devicewhich performs the optical scanning of the photosensitive surface ofsaid image carrying body as the surface to be scanned.
 31. The imageforming apparatus as claimed in claim 25, wherein said optical scanningdevice comprises a light deflector which deflects the light flux fromthe light source, wherein: said light deflector has a deflectionreflecting surface and deflects the light flux at a uniform angularvelocity; and said optical scanning lens has a function of causing thescanning of said surface to be scanned to be performed at a uniformvelocity.
 32. The image forming apparatus as claimed in claim 26,wherein said optical scanning device comprises a light deflector whichdeflects the light flux from the light source, wherein: said lightdeflector has a deflection reflecting surface and deflects the lightflux at a uniform angular velocity; and said optical scanning lens has afunction of causing the scanning of said surface to be scanned to beperformed at a uniform velocity.
 33. The image forming apparatus asclaimed in claim 27, wherein said optical scanning device comprises alight deflector which deflects the light flux from the light source,wherein: said light deflector has a deflection reflecting surface anddeflects the light flux at a uniform angular velocity; and said opticalscanning lens has a function of causing the scanning of said surface tobe scanned to be performed at a uniform velocity.
 34. The image formingapparatus as claimed in claim 28, wherein said optical scanning devicecomprises a light deflector which deflects the light flux from the lightsource, wherein: said light deflector has a deflection reflectingsurface and deflects the light flux at a uniform angular velocity; andsaid optical scanning lens has a function of causing the scanning ofsaid surface to be scanned to be performed at a uniform velocity. 35.The image forming apparatus as claimed in claim 29, wherein said opticalscanning device comprises a light deflector which deflects the lightflux from the light source, wherein: said light deflector has adeflection reflecting surface and deflects the light flux at a uniformangular velocity; and said optical scanning lens has a function ofcausing the scanning of said surface to be scanned to be performed at auniform velocity.
 36. The image forming apparatus as claimed in claim30, wherein said optical scanning device comprises a light deflectorwhich deflects the light flux from the light source, wherein: said lightdeflector has a deflection reflecting surface and deflects the lightflux at a uniform angular velocity; and said optical scanning lens has afunction of causing the scanning of said surface to be scanned to beperformed at a uniform velocity.
 37. The image forming apparatus asclaimed in claim 31 wherein, in said optical scanning device, an imageis formed from the light flux from the light source in the vicinity ofthe deflection reflecting surface of said light deflector, said imagebeing like approximately a line long in main scanning directions. 38.The image forming apparatus as claimed in claim 32 wherein, in saidoptical scanning device, an image is formed from the light flux from thelight source in the vicinity of the deflection reflecting surface ofsaid light deflector, said image being like approximately a line long inmain scanning directions.
 39. The image forming apparatus as claimed inclaim 33 wherein, in said optical scanning device, an image is formedfrom the light flux from the light source in the vicinity of thedeflection reflecting surface of said light deflector, said image beinglike approximately a line long in main scanning directions.
 40. Theimage forming apparatus as claimed in claim 34 wherein, in said opticalscanning device, an image is formed from the light flux from the lightsource in the vicinity of the deflection reflecting surface of saidlight deflector, said image being like approximately a line long in mainscanning directions.
 41. The image forming apparatus as claimed in claim35 wherein, in said optical scanning device, an image is formed from thelight flux from the light source in the vicinity of the deflectionreflecting surface of said light deflector, said image being likeapproximately a line long in main scanning directions.
 42. The imageforming apparatus as claimed in claim 36 wherein, in said opticalscanning device, an image is formed from the light flux from the lightsource in the vicinity of the deflection reflecting surface of saidlight deflector, said image being like approximately a line long in mainscanning directions.
 43. The image forming apparatus as claimed in claim25, wherein said image carrying body is a photoconductive photosensitivebody, after the photosensitive surface being charged uniformly, anelectrostatic latent image being formed thereon by the optical scanning,the thus-formed electrostatic latent image being developed so that atoner image is obtained, and the thus-obtained toner image beingtransferred and fixed onto a sheet-like recording medium.
 44. The imageforming apparatus as claimed in claim 26, wherein said image carryingbody is a photoconductive photosensitive body, after the photosensitivesurface being charged uniformly, an electrostatic latent image beingformed thereon by the optical scanning, the thus-formed electrostaticlatent image being developed so that a toner image is obtained, and thethus-obtained toner image being transferred and fixed onto a sheet-likerecording medium.
 45. The image forming apparatus as claimed in claim27, wherein said image carrying body is a photoconductive photosensitivebody, after the photosensitive surface being charged uniformly, anelectrostatic latent image being formed thereon by the optical scanning,the thus-formed electrostatic latent image being developed so that atoner image is obtained, and the thus-obtained toner image beingtransferred and fixed onto a sheet-like recording medium.
 46. The imageforming apparatus as claimed in claim 28, wherein said image carryingbody is a photoconductive photosensitive body, after the photosensitivesurface being charged uniformly, an electrostatic latent image beingformed thereon by the optical scanning, the thus-formed electrostaticlatent image being developed so that a toner image is obtained, and thethus-obtained toner image being transferred and fixed onto a sheet-likerecording medium.
 47. The image forming apparatus as claimed in claim29, wherein said image carrying body is a photoconductive photosensitivebody, after the photosensitive surface being charged uniformly, anelectrostatic latent image being formed thereon by the optical scanning,the thus-formed electrostatic latent image being developed so that atoner image is obtained, and the thus-obtained toner image beingtransferred and fixed onto a sheet-like recording medium.
 48. The imageforming apparatus as claimed in claim 30, wherein said image carryingbody is a photoconductive photosensitive body, after the photosensitivesurface being charged uniformly, an electrostatic latent image beingformed thereon by the optical scanning, the thus-formed electrostaticlatent image being developed so that a toner image is obtained, and thethus-obtained toner image being transferred and fixed onto a sheet-likerecording medium.
 49. An optical scanning lens which is used in ascanning and image forming optical system which gathers a light fluxdeflected by a light deflector in the vicinity of a surface to bescanned, wherein: said lens is formed by a resin having the followingproperties: photoelasticity constant≦8 (10⁻¹³cm²/dyne); saturationmoisture absorption≦0.5(%); and mold shrinkage coefficient≧0.7(%), andthe following condition is satisfied: 1.487×d ²/λ≧{β/(β−1)·L}²·(2·Δn·t), where: d denotes a beam diameter defined by 1/e2 the peakintensity thereof; λ denotes a wavelength; β denotes a lateralmagnification of said lens; L denotes a distance between the deflectionsurface of the optical deflector and the surface to be scanned; and Δndenotes a quadratic coefficient of refractive-index distributionapproximated from Δn(x) by a least squares method in quadratic formula,where Δn(x) denotes a refractive-index distribution existing in saidlens in a range of approximately ±1 mm from the center of the light fluxwithin a region which the light flux passes through, in said lens; and tdenotes a thickness of said lens.
 50. The optical scanning lens asclaimed in claim 49, wherein said lens is molded by using a metal die.51. The optical scanning lens as claimed in claim 49, wherein said resincomprises a polyolefin resin.
 52. An optical scanning device whichdeflects a light flux from a light source, gathers the deflected lightflux on a surface to be scanned by a scanning and image forming opticalsystem as a beam spot, wherein the optical scanning lens claimed inclaim 49 is applied in said scanning and image forming optical system.53. An image forming apparatus which performs optical scanning of aphotosensitive surface of an image carrying body and thereby forms alatent image thereon, wherein the optical scanning device claimed inclaim 52 is mounted as an optical scanning device which performs theoptical scanning of the photosensitive surface of said image carryingbody as the surface to be scanned.